---
title: "Laplace"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575240/Laplace"
format: markdown
---
Laplace(m,s) = m+Exponential(SQRT(2)/s)-Exponential(SQRT(2)/s)

[Laplace equations](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26576284/)

 

 

If X and Y are two identical independent Exponential(1/s) distributions, and if X is shifted m to the right of Y, then (X-Y) is a Laplace(m, s) distribution. The Laplace distribution has a strange shape with a sharp peak and tails that are longer than tails of a [Normal](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575246/) distribution. The figure below plots a Laplace(0,1) against a Normal(0,1) distribution:

 

 

![image](media://ddafd150-35c7-4870-b681-55b2eee82907)

 

 

 

#### Uses

The Laplace has found a variety of very specific uses, but they nearly all relate to the fact that it has long tails.

 

#### Generation

Crystal Ball does not have this distribution, but it can easily be generated as the difference between two identical [Exponential](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575227/) distributions as follows:

 

![image](media://97c74c36-312f-4733-975a-db796558f285)

 

> Macro (mathblock)

You can find an example in [Laplace](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575240/Laplace#Laplace) model.

> Macro (anchor)



The links to the Laplace software specific models are provided here:

<details>
<summary>Crystal Ball</summary>

> Macro (inline-media-image)

 [Laplace](/wiki/download/attachments/26579343/Laplace-CB.xlsx?version=1&modificationDate=1506113495000&cacheVersion=1&api=v2)
</details>

<details>
<summary>@Risk</summary>

> Macro (inline-media-image)

 [Laplace](/wiki/download/attachments/26581760/Laplace-AtRISK.xlsx?version=1&modificationDate=1506097513000&cacheVersion=1&api=v2)
</details>

 

#### Comments

When m = 0, and s = 1 we have the standard form of the Laplace distribution, which is also occasionally called "*Poisson's first law of error*'. The Laplace distribution is also known as the Double-Exponential distribution (though the Gumbel [Extreme Value](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575228/) distribution also takes this name), the *Two-Tailed Exponential* and the *Bilateral Exponential distribution*. [Skewness](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575508) = 0, [Kurtosis](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575509) = 6.

 

 

 

 

 

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